You can get a bolt-on receiver hitch for the Prius, which makes a wonderful support for a large screwdriver antenna. I recommend the Curt 11468, which is readily available online. To install it, remove the rear underbody plastic cover and the two rear shipping brackets, bolt on the hitch in place of the shipping brackets, and notch the plastic cover to go on over the hitch. Those are not towing brackets, by the way. The Prius has to be towed with its front wheels off of the ground. The brackets are used to ship a new Prius by train, with the front tilted up 90 degrees.
One nit about the Curt hitch, though: you may have to push hard on it to install it, as one of the side brackets on mine was a little too bent for the screw holes to line up without pushing. If that's the case, it will be a two-person install. That was the second one I tried. The first was even more severely bent due to a manufacturing process issue, and the holes didn't line up at all. I'm told that Curt stacks these hitches up to paint them, and that causes some of them to bend. I exchanged that unit for one without the bend.
I also tried the hitch from Coastal Technologies, and I'm afraid that I don't recommend it. It's too flexible, and using it with a bicycle rack (I've lots of hobbies) was precarious as the entire assembly drooped, bounced, etc. The curt has some flexibility too, but less. The Curt costs a bit less, it's tougher because there's more metal to it, and it doesn't come near enough to the muffler to have problems the Coastal has had with hitting the muffler. Of course, the wonderful folks at Coastal (hi Kelley) took the hitch right back. I asked for a credit and bought a Prius video input from them.
I have a Tarheel Antennas model 300, which - who knows why - isn't listed on their web site although they sold it at Hamvention 2006 and it's been reviewed extensively. Call them up and ask about this one, as it's the right size for the Prius. They sell all necessary brackets to mount it to a receiver hitch. They even had it in red, to match my Prius! It's tall enough to put the whip above the roofline of the Prius.